\(B=4\Rightarrow\dfrac{n+1}{n-2}=4\)

\(\Rightarrow n+1=4\left(n-2\right)\)

\(\Rightarrow n+1=4n-8\)

\(\Rightarrow4n-n=1+8\)

\(\Rightarrow3n=9\)

\(\Rightarrow n=3\)

b.

\(B=-\dfrac{1}{2}\Rightarrow\dfrac{n+1}{n-2}=-\dfrac{1}{2}\)

\(\Rightarrow n-2=-2\left(n+1\right)\)

\(\Rightarrow n-2=-2n-2\)

\(\Rightarrow n+2n=2-2\)

\(\Rightarrow3n=0\)

\(\Rightarrow n=0\)

\(B=4\\ \Leftrightarrow\dfrac{n+1}{n-2}=4\\ \Leftrightarrow4n+4=n-2\\ \Leftrightarrow4n-n=-2-4\\ \Leftrightarrow3n=-6\\ \Leftrightarrow n=-2\\ B=\dfrac{-1}{2}\\ \Leftrightarrow\dfrac{n+1}{n-2}=\dfrac{-1}{2}\\ \Leftrightarrow2n+2=-n+2\\ \Leftrightarrow2x+n=2-2\\ \Leftrightarrow3n=0\\ \Leftrightarrow n=0\)

1-3+5-7+9-11+.......+2021-2023

=(1-3)+(5-7)+(9-11)+...+(2021-2023)

=(-2)+(-2)+(-2)+....+(-2) (có 506 số -2)

=506 x (-2)

=-1012

cảm ơn bạn nhé

\(6.3\\ \dfrac{8}{-11}=\dfrac{8.\left(-1\right)}{\left(-11\right).\left(-1\right)}=\dfrac{-8}{11};\dfrac{-5}{-9}=\dfrac{-5:\left(-1\right)}{\left(-9\right):\left(-1\right)}=\dfrac{5}{9}\\ --\\ 6.4\\ \dfrac{-12}{4}=\dfrac{-12:4}{4:4}=-3\\ \dfrac{7}{-35}=\dfrac{7:\left(-7\right)}{-35:\left(-7\right)}=-\dfrac{1}{5}\\ \dfrac{-9}{27}=\dfrac{-9:9}{27:9}=\dfrac{-1}{3}\)

\(6.5\\ 15p=\dfrac{15}{60}\left(h\right)=\dfrac{15:15}{60:15}\left(h\right)=\dfrac{1}{4}\left(h\right)\\ 90p=\dfrac{90}{60}\left(h\right)=\dfrac{90:30}{60:30}\left(h\right)=\dfrac{3}{2}\left(h\right)\)

Cảm ơn!

\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2024}}\\ =>2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2023}}\\ =>2A-A=A=1-\dfrac{1}{2^{2024}}=\dfrac{2^{2024}-1}{2^{2024}}\)

e cảm ơn

\(\dfrac{x}{-2}=-\dfrac{8}{x}\left(x\ne0\right)\\ =>x.x=\left(-2\right).\left(-8\right)\\ =>x^2=16\\ =>x=\pm4\)

\(\dfrac{x}{-2}=\dfrac{-8}{x}\\ x.x=\left(-8\right).\left(-2\right)=16=4.4=\left(-4\right).\left(-4\right)\\ Vậy:\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

\(\dfrac{x+3}{2015}+\dfrac{x+2}{2016}+\dfrac{x+1}{2017}+\dfrac{x}{1009}=-5\\ =>\left(\dfrac{x+3}{2015}+1\right)+\left(\dfrac{x+2}{2016}+1\right)+\left(\dfrac{x+1}{2017}+1\right)+\left(\dfrac{x}{1009}+2\right)=0\\ =>\dfrac{x+2018}{2015}+\dfrac{x+2018}{2016}+\dfrac{x+2018}{2017}+\dfrac{x+2018}{1009}=0\\ =>\left(x+2018\right)\left(\dfrac{1}{2015}+\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{1}{1009}\right)=0\\ =>x+2018=0\\ =>x=-2018\left(TM\right)\)

em cảm ơn

Bài còn lại mờ quá em ơi

Lời giải:

$2^{x+2}.3^2-3.5^2=69$

$2^{x+3}.9=69+3.5^2=144$

$2^{x+3}=144:9=16=2^4$

$\Rightarrow x+3=4$

$\Rightarrow x=1$

\(2^{x+2}.3^2-3.5^2=69\\ =>2^{x+2}.9-3.25=69\\ =>2^{x+2}.9=69+75=144\\ =>2^{x+2}=144:9\\ =>2^{x+2}=16=2^4\\ =>x+2=4\\ =>x=2\)

\(\left(-4\right)x=36\)

\(x=36:\left(-4\right)\)

\(x=-9\)

$\left(-4\right)x=36$

$x=36:\left(-4\right)$

$x=-9$

Lời giải:

$\frac{1}{50}> \frac{1}{100}$

$\frac{1}{51}> \frac{1}{100}$

.....

$\frac{1}{98}> \frac{1}{100}$

$\frac{1}{99}> \frac{1}{100}$

$\Rightarrow S> \underbrace{\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}}_{50}=\frac{1}{100}.50=\frac{1}{2}$